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Math Expert
Joined: 02 Sep 2009
Posts: 50579
Last year, Company X paid out a total of $1,050,000 in salaries to its [#permalink] ### Show Tags 20 Apr 2015, 06:53 2 11 00:00 Difficulty: 65% (hard) Question Stats: 56% (01:07) correct 44% (01:15) wrong based on 315 sessions ### HideShow timer Statistics Last year, Company X paid out a total of$1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000 (B)$41,667
(C) $42,000 (D)$50,000
(E) $60,000 Kudos for a correct solution. _________________ Retired Moderator Joined: 06 Jul 2014 Posts: 1241 Location: Ukraine Concentration: Entrepreneurship, Technology GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Re: Last year, Company X paid out a total of$1,050,000 in salaries to its  [#permalink]

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21 Apr 2015, 08:44
2
1
Bunuel wrote:
Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned? (A)$40,000
(B) $41,667 (C)$42,000
(D) $50,000 (E)$60,000

Kudos for a correct solution.

Let's imagine that $$x$$ is max salary and $$\frac{x}{1.2}$$ is min salary.
As we know that total amount of salary equal to 1,050,000 we can write equation:
$$20x+\frac{x}{1.2}=1,050,000$$ (20 employees with max salary and one with min salary: if we take 20 employees with min salary we will receive bigger number and as we need least possible salary we should take 20 max salaries)
$$24x + x = 12,600,000$$
$$x = 50,400$$ and this is max salary
$$50,400 / 1.2 = 42000$$

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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its [#permalink] ### Show Tags 21 Apr 2015, 20:41 2 Hi All, This question is remarkably similar to the following Official GMAC question: a-certain-city-with-a-population-of-132-000-is-to-be-divided-into-11-v-191085.html?hilit=population%20GREATEST#p1464387 The various methods to solve it are exactly the same (including the opportunity to TEST THE ANSWERS). GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Joined: 15 May 2014
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22 Apr 2015, 05:36
1
Let x be the minimum salary,

Therefore, the maximum salary would be x * 0.2 + x = 1.2x
To get the minimum value for x, we have to maximise the value of all the other salaries, therefore we make all the other 20 people earn 1.2x

Total Amount
So we have x + 20(1.2x) = 1,050,000
x+ 24x = 1,050,000
25x = 1,050,000
x = 42,000
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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its [#permalink] ### Show Tags 22 Apr 2015, 08:55 2 [quote="Bunuel"]Last year, Company X paid out a total of$1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000 (B)$41,667
(C) $42,000 (D)$50,000
(E) $60,000 Employee 1 earned$x(say)
Employee 2 will not earn more than $1.2x Therfore, to minimize the salary of any one employee, we need to maximize the salaries of the other 20 employees (1.2x*20)+x=1,050,000 Solving for x=$42,000
Math Expert
Joined: 02 Sep 2009
Posts: 50579
Re: Last year, Company X paid out a total of $1,050,000 in salaries to its [#permalink] ### Show Tags 27 Apr 2015, 02:53 Bunuel wrote: Last year, Company X paid out a total of$1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000 (B)$41,667
(C) $42,000 (D)$50,000
(E) $60,000 Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION: Here ask yourself the following questions: 1) The numbers do not have to be integers. 2) Zero is theoretically possible (but probably constrained by the 20% difference restriction) 3) Numbers absolutely can repeat (which will be very important) 4) What’s your strategy? If you want the LOWEST possible single salary, then use your answer to #3 (they can repeat) and give the other 20 salaries the maximum. That way your calculation looks like: x + 20(1.2x) = 1,050,000 Which breaks out to 25x = 1,050,000, and x = 42000. And notice how important the answer to #3 was – by knowing that numbers could repeat, you were able to quickly put together a smart strategy to minimize one single value. The larger lesson is crucial here, though – these problems are often (but not always) fairly basic mathematically, but derive their difficulty from a situation that limits some options or allows for more than you’d think via integer restrictions, the possibility of zero, and the possibility of repeat values. Ask yourself these four questions, and your answer to the first three especially will maximize your efficiency on the strategic portion of the problem. _________________ Current Student Joined: 12 Aug 2015 Posts: 287 Concentration: General Management, Operations GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27 GPA: 3.3 WE: Management Consulting (Consulting) Re: Last year, Company X paid out a total of$1,050,000 in salaries to its  [#permalink]

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23 Jan 2016, 02:50
Back-solving.

Use answer D: if minimum is 50k then 20% greater than that is 60k. Calculate whether the total salary base matches with that: 60*20+50 = way too much.

Use answer A (B is ugly so let us leave it for now): 40 + 48*20 = 1000 -> too little

Let us test C (B is ugly): 42 + 42*1.2*20 = 1050. Bingo!
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Re: Last year, Company X paid out a total of $1,050,000 in salaries to its [#permalink] ### Show Tags 06 Feb 2018, 17:36 Bunuel wrote: Last year, Company X paid out a total of$1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?

(A) $40,000 (B)$41,667
(C) $42,000 (D)$50,000
(E) $60,000 Since the sum of all the salaries is a fixed amount (which is given to be$1,050,000), the lowest possible salary is obtained when all the salaries besides the lowest one are maximized. Since the greatest possible difference between any two salaries in this company is 20%, all the salaries besides the lowest salary should be 20% more than the lowest salary.

We can let the lowest salary = x and the greatest = 1.2x and create the following equation:

x + 20(1.2x) = 1,050,000

x + 24x = 1,050,000

25x = 1,050,000

x = 42,000

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01 Oct 2018, 23:49
Quote:
Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned? (A)$40,000
(B) $41,667 (C)$42,000
(D) $50,000 (E)$60,000
This is a min/max problem can be attacked several different ways.
If the goal is to find the minimum possible salary among the 21 employees then you want to maximize the salary of 20 employees and see how much is left for the one remaining person with the lowest salary.

Since no salary can be more than 20% greater than any other, you want to assign the low salary as x and the remaining 20 salaries as 1.2x (20% greater than x).

The total salaries would then be x + 20(1.2x) = 25x. Dividing $1,050,000 by 25 you see that the lowest salary would be$42,000

Alternatively:
Quote:
Also on this problem, you could back solve using the same logic: start with C and multiply it by 1.2 to get $50,400. If you multiply$50,400 by 20 and add $42,000 you get the required total of$1,050,000.

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22 Oct 2018, 01:06
asthagupta wrote:
I am still not sure why we are taking 20 with max salary and 1 with lowest salary. By any means the max difference can come even if we take 1 person with max and 20 with min.

Hi asthagupta,
https://gmatclub.com/forum/a-certain-ci ... 76217.html

Please check the explanation of Bunuel in the above link(OG Question), you may raise further specific queries (if any).
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